Parameters effecting the yield of NO_x per joule

An NO_x freeze out mixing ratio of (2.3±0.3)% was also determined at 67 mbar pressure, using a much smaller reaction vessel (volume = 21.5 cm³) to circumvent some of the problems previously mentioned. However, for this case, the calculated volume of unperturbed gas heated to the freeze out temperature was comparable with the volume of the reactor, implying that some of the heat in the gas could be lost to the reactor walls, even while the gas temperature was high (above 2000 K), giving a reduction in NO_x formed. This was confirmed by firing discharges with the same conditions in both the small and large reactors, the larger reactor produced approximately twice as much NO_x per unit energy stored on the capacitor (P). Increasing the reactor size above 250 cm³ had little further effect on the NO_x yield.

A more common problem with laboratory determinations of P is heat loss to the electrodes. This was examined in two ways. Firstly, when the electrode diameter was increased from 4 to 12 mm, the quantity of NO_x formed was found to be reduced by a factor of two, even though all other parameters remained fixed. Secondly, the spark gap was increased from 4 to 20 mm (figure 4) giving a three fold increase in NO_x formed per unit energy (stored on the capacitor). This behaviour is consistent with some of the energy of the gas being lost to the electrodes. This has in fact been demonstrated by Roth et al. [1951] who measured the decay with time of the fraction of heat (F) remaining in the gas between a spark gap. As the heat is lost (ideally) along only one space coordinate, F was determined in terms of a universal dimensionless parameter upsilon, which is the product of the thermal diffusivity constant, K (0.18 cm²s^-1 for O₂ at STP), the time since the discharge, t, divided by the square of the spark gap, d²:

                Kt  
    upsilon  =  --                (4)
                d2

F(upsilon) approaches 100% as upsilon approaches zero and for 4.6 mm diameter electrodes they found that F(upsilon) drops to ca. 10% for upsilon ca. 0.5.

Assuming that all the energy from the capacitor is transferred to the gas in the spark gap initially, the quantity of NO_x formed (N) will be the product of the yield of NO_x per joule (P) and the fraction (F) of energy (˝CV²) remaining in the hot channel by the time it has cooled to the freeze out temperature:

The time (t) for the gases in the hot channel to cool to the freeze out temperature is not known, but assuming a value of ca. 10^-1 s the fraction of heat remaining in the gas between the spark gap can be determined from Roth et al's analysis as approximately 10% for a 4 mm spark gap, rising to 50% for a 20 mm gap (using t = 10^-2 s gives F(4mm) = 35%, rising to F(20mm) = 70%).

Also, increasing the ambient pressure from 0.13 bar to 1.0 bar gave an increase in NO_x per unit energy of 45%. In the analysis of Roth el al. [1951] the heat loss dimensionless parameter, upsilon, is dependent on pressure via the thermal diffusion constant K which is inversely proportional to the pressure. Using their relationship between F and with an assumed value of t of 10^-1 s gives F = 15% at 130 mbar rising to 40% at 1013 mbar (for t = 10^-2 s, F(130 mbar) = 45%, rising to F(1 bar) = 65%).

Due to uncertainties in the time to cool to the freeze out temperature, this analysis cannot be used to accurately determine F (and consequently P). However significant loss of heat to the electrodes is consistent with both our comparatively low measured values of NO_x per unit energy stored on the capacitor, and its increase with increasing spark gap and pressure, and again suggests that the gas in which the NO_x is formed is cooling far slower than either the duration of the discharge or the shock front.

The main circuit element that effected NO_x formation was the thyratron, removing it from the circuit increased the NO_x yield per unit energy (stored on the capacitor) by a factor of 2.5. The implication is that a significant fraction of the energy stored on the capacitor was not transferred to the spark gap, but to the thyratron. Consequently, the thyratron was not used in the experiments shown in figures 1, 2 , 4 and 5 .